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.. _appendix_on_units:
On Units
********
As previously stated, in this module you will find two very similar
sets of classes available. These are the **NIST** and **SI**
prefixes. The **NIST** prefixes are all base 2 and have an 'i'
character in the middle. The **SI** prefixes are base 10 and have no
'i' character.
For smaller values, these two systems of unit prefixes are roughly
equivalent. The ``round()`` operations below demonstrate how close in
a percent one "unit" of SI is to one "unit" of NIST.
.. code-block:: python
:linenos:
:emphasize-lines: 7,15,23
In [15]: one_kilo = 1 * 10**3
In [16]: one_kibi = 1 * 2**10
In [17]: round(one_kilo / float(one_kibi), 2)
Out[17]: 0.98
In [18]: one_tera = 1 * 10**12
In [19]: one_tebi = 1 * 2**40
In [20]: round(one_tera / float(one_tebi), 2)
Out[20]: 0.91
In [21]: one_exa = 1 * 10**18
In [22]: one_exbi = 1 * 2**60
In [23]: round(one_exa / float(one_exbi), 2)
Out[23]: 0.87
They begin as roughly equivalent, however as you can see (lines:
**7**, **15**, and **23**), they diverge significantly for higher
values.
Why two unit systems? Why take the time to point this difference out?
Why should you care? `The Linux Documentation Project
<http://www.tldp.org/>`_ comments on that:
Before these binary prefixes were introduced, it was fairly common
to use k=1000 and K=1024, just like b=bit, B=byte. Unfortunately,
the M is capital already, and cannot be capitalized to indicate
binary-ness.
At first that didn't matter too much, since memory modules and
disks came in sizes that were powers of two, so everyone knew that
in such contexts "kilobyte" and "megabyte" meant 1024 and 1048576
bytes, respectively. What originally was a sloppy use of the
prefixes "kilo" and "mega" started to become regarded as the "real
true meaning" when computers were involved. But then disk
technology changed, and disk sizes became arbitrary numbers.
After a period of uncertainty all disk manufacturers settled on
the standard, namely k=1000, M=1000k, G=1000M.
The situation was messy: in the 14k4 modems, k=1000; in the 1.44MB
diskettes, M=1024000; etc. In 1998 the IEC approved the standard
that defines the binary prefixes given above, enabling people to
be precise and unambiguous.
Thus, today, MB = 1000000B and MiB = 1048576B.
In the free software world programs are slowly being changed to
conform. When the Linux kernel boots and says::
hda: 120064896 sectors (61473 MB) w/2048KiB Cache
the MB are megabytes and the KiB are kibibytes.
- Source: ``man 7 units`` - http://man7.org/linux/man-pages/man7/units.7.html
Furthermore, to quote the `National Institute of Standards and
Technology (NIST) <http://physics.nist.gov/cuu/Units/binary.html>`_:
"Once upon a time, computer professionals noticed that 2\ :sup:`10` was
very nearly equal to 1000 and started using the SI prefix "kilo"
to mean 1024. That worked well enough for a decade or two because
everybody who talked kilobytes knew that the term implied 1024
bytes. But, almost overnight a much more numerous "everybody"
bought computers, and the trade computer professionals needed to
talk to physicists and engineers and even to ordinary people, most
of whom know that a kilometer is 1000 meters and a kilogram is
1000 grams.
"Then data storage for gigabytes, and even terabytes, became
practical, and the storage devices were not constructed on binary
trees, which meant that, for many practical purposes, binary
arithmetic was less convenient than decimal arithmetic. The result
is that today "everybody" does not "know" what a megabyte is. When
discussing computer memory, most manufacturers use megabyte to
mean 2\ :sup:`20` = 1 048 576 bytes, but the manufacturers of computer
storage devices usually use the term to mean 1 000 000 bytes. Some
designers of local area networks have used megabit per second to
mean 1 048 576 bit/s, but all telecommunications engineers use it
to mean 106 bit/s. And if two definitions of the megabyte are not
enough, a third megabyte of 1 024 000 bytes is the megabyte used
to format the familiar 90 mm (3 1/2 inch), "1.44 MB" diskette. The
confusion is real, as is the potential for incompatibility in
standards and in implemented systems.
"Faced with this reality, the IEEE Standards Board decided that
IEEE standards will use the conventional, internationally adopted,
definitions of the SI prefixes. Mega will mean 1 000 000, except
that the base-two definition may be used (if such usage is
explicitly pointed out on a case-by-case basis) until such time
that prefixes for binary multiples are adopted by an appropriate
standards body."
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